082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

2.4 Review of some common engineering functions and techniques 99
17 Byusinglog--linear paper findthe relationship
betweenxandygiven the following table ofvalues:
x 1.5 1.7 3.2 3.9 4.3 4.9
y 8.5 9.7 27.6 44.8 59.1 89.6
18 Byusinglog--logpaper findthe relationshipbetween
x andygiven the following table ofvalues:
x 2.0 2.5 3.0 3.5 4.0 4.5
y 13.0 19.0 25.9 33.6 42.2 51.6
Solutions
1 (a) 3 (b) 3.9069
(c) 1.4110 (d) 1.7356
(e) 1.5079 (f) 1.8515
2 (a) log7x (b) logxyz
( )
y
(c) ln (d) logxy 2
3
( )
(e) ln(xy 3 x +y
) (f) ln
y
(g) log8x 3 (h) logx 2 y 3
(i) log1 = 0 (j) lnx 3 y 2 z 4
( ) ( )
y 3 z t 4 (k) log
x 2 (l) log
2
3 (a) 2lntorlnt 2 (b) 16logt
( )
y 7 (c) ln (d) ln2
3
( )
9x 3/2
(e) log
2
5 (a) 4.2485 (b) −1.0986
(c) 0 (d) 2.8134
(e) 1.3040 (f) 1.3519
(g) 1.2877 (h) 1.1094
(i) 1.3863 (j) 0.6094
(k) 1.7661 (l) 0.6931
(m) 1.7329 (n) 1.5404
(o) 1.9459 (p) −1.5041
(q) 0.6931 (r) −0.9808
(s) 0, 0.6931
(t) −0.6931,1.0986
(u) 0.6931,1.0986 (v) 1.0986,1.3863
6 (a) 1.4771 (b) −0.6021
(c) 0.6990 (d) 0.9771
(e) 1.1003 (f) −1.9208
(g) 0.5663 (h) 0.3495
(i) 3.3010 (j) 0.2917
(k) −0.1761 (l) −0.8010
(m) 0.2386 (n) −0.3010
(o) 0.6395 (p) 0.4924
(q) 0.3473 (r) −0.0739
(s) 0.3010,0.6990 (t) 0.3010
(u) 0.3010,0.4771 (v) −0.3010,0.1761
7 (a) 39.81 (b) 19.91 (c) 37.81
(d) ±3.98 (e) 4.01
8 (a) 11.02 (b) 18.20 (c) 6.59
(d) ±6.71 (e) 6.38
9 (a) 1.0148 (b) −0.4130 (c) −0.2877
(d) −1.3863 (e) 1.3117 (f) 2.0553
(g) 0.5485
10 (a) 20dB (b) 80 dB (c) 64.1 dB
(d) 30.46dB
11 Preamplifier gain = 26.02 dB, mainamplifiergain
= 17.50 dB,total gain = 43.52 dB
12 10 −3 W or1mW
13 60 dBm
14 20 µPa
15 0.011Paor11 mPa
16 10 5 or100 kPa
17 y=3(2 x )
18 y = 4x 1.7